General Pattern Theory
A Mathematical Study of Regular Structures
Series: Oxford Mathematical Monographs;
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Product details:
- Publisher Clarendon Press
- Date of Publication 20 January 1994
- ISBN 9780198536710
- Binding Hardback
- No. of pages906 pages
- Size 249x196x49 mm
- Weight 1706 g
- Language English
- Illustrations 16 colour plates, numerous black and white figures, tables 0
Categories
Short description:
The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world.
MoreLong description:
The aim of pattern theory is to create mathematical knowledge representations of complex systems, analyse the mathematical properties of the resulting regular structures, and to apply them to practically occuring patterns in nature and the man-made world. Starting from an algebraic formulation of such representations they are studied in terms of their topological, dynamical and probabilistic aspects. Patterns are expressed through their typical behaviour as well as through their variability around their typical form. Employing the representations (regular structures) algorithms are derived for the understanding, recognition, and restoration of observed patterns. The algorithms are investigated through computer experiments.
this is an important book that should richly reward the persistent reader
Table of Contents:
Part I: Pattern Algebra
Generators and configurations
Images and patterns
Part II: Pattern Topology
Some topologies on regular structures
Part III: Pattern Dynamics
Abstract biological patterns
Patterns of collective behaviour
Patterns generated from extremum principles
Part IV: Metric Pattern Theory
General principles of MPT
Pattern synthesis
First limit problem in MPT
Second limit problem in MPT
Mixed limit problem in MPT
Part V: Pattern Deformations
Chapter 12: Deformation mechanisms
Part VI: Pattern Inference
Ends and means in pattern analysis
Bayesian pattern inference
Lattice-based models
Continuum-based models
Non-Bayesian pattern inference
Pattern recognition
Part VII: Creating Regular Structures
Creating generators
Creating acceptor functions and connectors
